PHD Thesis - Institute for Computer Graphics and Vision - Graz ...

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165 Trilinearities Line-line-line correspondence Point-line-line correspondence Point-line-point correspondence (l r ɛ ris )l ′ j l′′ T jk k i = 0 s x i l ′ j l′′ k T jk i = 0 x i l ′ j (x′′k ɛ kqs )T jq i = 0 s Point-point-line correspondence x i (x ′j ɛ jpr )l ′′ T pk k i = 0 r Point-point-point correspondence x i (x ′j ɛ jpr )(x ′′k ɛ kqs )T pq i = 0 rs Table B.1: Summary of the incidence relations (trilinearities) imposed by the trifocal tensor. 2. Next compute the line l’ through ̂x ′ which should be perpendicular to the epipolar line of ̂x which is defined by l ′ e = F 21̂x. Then l ′ = (l 2 , −l 1 , −̂x 1 l 2 + ̂x 2 l 1 ) T with l ′ e = (l 1 , l 2 , l 3 ) T and ̂x ′ = (̂x 1 , ̂x 2 , 1) T . 3. The transferred point is x ′′k = ̂x i l ′ j T jk i where l ′ j T jk i is the homography mapping H k i =H 13(l ′ ). The point transfer for the other views works similar and the corresponding equations are given in Table B.2. view 2,3→1 view 1,3→2 view 1,2→3 l ′ e = F T 21̂x′′ l ′′ e = F 31̂x l ′ e = F 21̂x l ′ = (l 2 , −l 1 , −̂x ′′ 1 l 2 + ̂x ′′ 2 l 1) T l ′′ = (l 2 , −l 1 , −̂x 1 l 2 + ̂x 2 l 1 ) T l ′ = (l 2 , −l 1 , −̂x 1 l 2 + ̂x 2 l 1 ) T H 13 (l ′ ) = H k i =l ′ j T jk i H 12 (l ′′ ) = H j i =l′′ k T jk i H 13 (l ′ ) = Hi k =l j ′ T jk i x = H 13 (l ′ ) −1 x ′′ x ′ = H 12 (l ′′ )x x ′′ = H 13 (l ′ )x Table B.2: Relations to transfer a point into each view using the trifocal tensor.
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Graz University of Technology Insti
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Abstract Visual map building and lo
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Contents 1 Introduction to mobile r
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CONTENTS vi 7.1.5 Sub-map linking .
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1.1. Localization and map building
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1.3. What has already been achieved
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1.5. How can it get solved? 6 fully
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1.6. Contribution of this thesis 8
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1.7. Structure of the thesis 10 com
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2.2. Localization from point featur
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2.2. Localization from point featur
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2.4. Localization from plane featur
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2.5. Summary 18 or not. Clearly thi
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Chapter 3 Local detectors Research
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3.1. Interest point detectors 22 fu
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3.2. Scale invariant detectors 24 r
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3.2. Scale invariant detectors 26 (
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3.2. Scale invariant detectors 28 3
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3.3. Affine invariant detectors 30
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3.4. Comparison of the described me
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3.4. Comparison of the described me
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44 But using a plane to plane homog
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4.2. Representation of the detectio
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4.3. Detection correspondence 48 th
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4.4. Point transfer using the trifo
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4.5. Ground truth generation 52 usi
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4.6. Experimental evaluation 54 Fig
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4.6. Experimental evaluation 56 rep
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4.6. Experimental evaluation 58 MSE
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4.6. Experimental evaluation 60 mat
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4.6. Experimental evaluation 62 vie
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4.6. Experimental evaluation 64 vie
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4.6. Experimental evaluation 66 rel
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Chapter 5 Maximally Stable Corner C
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5.1. The MSCC detector 70 (a) (b) (
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5.2. Region representation 72 400 (
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5.3. Computational complexity 74 6.
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5.5. Detection examples 76 paramete
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5.5. Detection examples 78 Figure 5
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5.6. Detector evaluation: Repeatabi
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5.7. Combining MSCC with other loca
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6.1. Wide-baseline region matching
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6.1. Wide-baseline region matching
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6.2. Piece-wise planar scene recons
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Chapter 7 Living in a piecewise pla
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7.1. Map building 112 s,R,t sub-map
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